Related papers: Connected, not separably connected complete metric…
In a spherically complete ultrametric space, a strictly contracting mapping has a fixed point. We indicate in this paper how this fixed point can either be reached or approximated.
We first prove that for all compact metrizable spaces, there exists a topological embedding of the compact metrizable space into each of the sets of compact metric spaces which are connected, path-connected, geodesic, or CAT(0), in the…
We construct a universal space for the class of proper metric spaces of bounded geometry and of given asymptotic dimension. As a consequence of this result, we establish coincidence of the asymptotic dimension with the asymptotic inductive…
In this paper, for a metrizable space $Z$, we consider the space of metrics that generate the same topology of $Z$, and that space of metrics is equipped with the supremum metrics. For a metrizable space $X$ and a closed subset $A$ of it,…
We study computable topological spaces and semicomputable and computable sets in these spaces. In particular, we investigate conditions under which semicomputable sets are computable. We prove that a semicomputable compact manifold $M$ is…
For every countable ordinal number $\xi$, we construct a metric space $X_{\xi}$ whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $\xi$.
In this paper (as in [Ken15]), we consider an effective version of the characterization of separable metric spaces as zero-dimensional iff every nonempty closed subset is a retract of the space (actually, it is a relative result for closed…
The completeness properties of spaces of immersed curves equipped with reparametrization-invariant Riemannian metrics have recently been the subject of active research. This thesis studies the metric completion of spaces of immersed open…
We define scoring metrics on separable metric spaces and show that they are always no coarser than the metrics from which they spring.
We show that any compact connected semialgebraic set is the projection of a connected component of the configuration space of a linkage.
We study the subsets of metric spaces that are negligible for the infimal length of connecting curves; such sets are called metrically removable. In particular, we show that every totally disconnected set with finite Hausdorff measure of…
This paper is concerned with conditions under which a metric continuum (a compact connected metric space) contains a non-degenerate chainable continuum.
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be…
We revisit the definition of effective local compactness, and propose an approach that works for arbitrary countably-based spaces extending the previous work on computable metric spaces. We use this to show that effective local compactness…
Using the wedge sum of metric spaces, for all compact metrizable spaces, we construct a topological embedding of the compact metrizable space into the set of all metric trees in the Gromov--Hausdorff space with finite prescribed values. As…
The space of unitary $C_{0}$-semigroups on separable infinite dimensional Hilbert space, when viewed under the topology of uniform weak convergence on compact subsets of $\mathbb{R}_{+}$, is known to admit various interesting residual…
We prove that every proper $n$-dimensional length metric space admits an "approximate isometric embedding" into Lorentzian space $\mathbb{R}^{3n+6,1}$. By an "approximate isometric embedding" we mean an embedding which preserves the energy…
We study different notions of connected constructive metric spaces. They differ the types of connected components and how different components relate to each other. These notions are equivalent in classical point set topology but they give…
We begin to study classical dimension theory from the computable analysis (TTE) point of view. For computable metric spaces, several effectivisations of zero-dimensionality are shown to be equivalent. The part of this characterisation that…